Blame-Game Politics in a Coalition Government1
Arnaud Dellis∗
∗ University of Hawaii - Manoa, Department of Economics, 2424 Maile Way,
Honolulu, HI 96822, USA
E-mail: [email protected]
Version: August 2005
An important question in political economics concerns delays in the adoption of socially
beneficial reforms. The present paper explores this issue in the context of a representative
democracy where the government is a coalition and citizens observe neither the decisionmaking process, nor the policy preferences of the politicians. It shows that a governing
party favoring a reform may nonetheless choose to veto its adoption and blame its coalition
partners for the non-adoption. This is referred to as blame-game politics. The rationale
for playing such a game is to prevent some parties from acquiring a better reputation
as supporters of the reform. At a more general level, the argument applies to situations
where several agents, whose types are private information have each to take an action
while the principal observes only the aggregate outcome.
Key Words: Reputation; Delayed adoption of reforms; Coalition Government.
JEL Classification: D7; D82; H0.
1. INTRODUCTION
There is a large body of literature that studies delays in the adoption of reforms.
But surprisingly enough only a relatively small portion of it looks at that problem in
the context of coalition governments, which however are well-known for the difficulty
they have in quickly passing reforms.2 Now there is nothing really puzzling in the
delayed adoption of a reform that benefits only a minority. What is baffling is when
the reform benefits a majority, and even more if it is also socially desirable. The
present work considers such a (welfare-enhancing) majority-preferred reform, and
provides an explanation for why a coalition government may delay the adoption of
such a reform, even if all its members would, as citizens, benefit from the reform.
The positive economic literature has yielded two explanations for the delayed
adoption of reforms by coalition governments. One explanation is the instability
of those governments, which implies that coalition members do not have enough
incentives to cooperate. For example consider a coalition member who has been
proposed the following deal: if he let pass the currently-debated reform that hurts
him but benefits his coalition partner, the latter commits that he will not veto
the adoption of another reform that benefits our coalition member but hurts his
coalition partner. Now our coalition member will be very reluctant to accept this
1 I would like to thank Steve Coate for his invaluable support and comments. I am
also grateful to Georges Casamatta, Ted O’Donoghue, Christoph Vanberg, and seminar
participants, for helpful comments.
2 For example Roubini and Sachs (1989) and Grilli et al. (1991) show that often coalition
governments are associated with large budget deficits, which they interpret as suggesting the
difficulty those governments have of quickly enacting reforms.
1
deal if he anticipates that the coalition is going to break soon. Indeed by the time
his reform will be on the agenda, there is a good chance that the government will
no longer be in office. The second explanation is that cabinet ministers may have
difficulties reaching an agreement on a reform because of ideological differences on
that issue or conflicts on how to share the cost of the reform. For example, a
conservative politician may veto a tax increase, especially one which is targeted
towards the electorate he represents.
One feature those two explanations share in common is that they both rely
on the heterogeneity of preferences among coalition members. Hence they cannot
explain the delayed adoption of a reform considered as desirable by all cabinet
members, a situation that we sometimes observe. For example between 1997 and
2002 the French government was divided between Prime Minister Jospin and President Chirac, both being responsible for the policies implemented. By the end of
their term in office, homeland security reforms - considered as desirable by a vast
majority of the population, and on which both Jospin and Chirac seemed to agree
- had not yet been adopted. Also, in 1999 a new coalition government was formed
in Belgium. At that time one prominent issue on the agenda was a reform of the
judicial system, reform which was asked by an overwhelming majority of the population and on the desirability of which all coalition members agreed. Four years
later, just before the next general election, the reform had not yet been adopted.
Hence we are left without any explanation for why a stable coalition government
sometimes delays the adoption of a reform that benefits all its members as well as
a majority of the population. The contribution of the present paper is to fill this
gap.
But before going further, it is worth making two observations. First it is commonplace to hear politicians blaming their fellows for the non-adoption of a reform.
This had been the case in the two examples discussed above. Indeed during the
2002 presidential election campaign in France Chirac blamed Jospin for the nonadoption of homeland security reforms. And at the beginning of May 2003, two
weeks before the general election, the two major parties in the Belgian coalition government were blaming each other for the non-adoption of the reform of the judicial
system. A second observation concerns the rules under which coalition governments traditionally operate. In a large number of countries where the government
is a coalition, the adoption of a decision requires either unanimity or a consensus
among cabinet members.3 This means that each governing party has the power to
block the adoption of a reform. Another rule under which coalition governments
usually operate is collective responsibility. This means that all cabinet members
bear the responsibility for the policies that are (or are not) adopted. It also implies
that, while in office, a minister is not supposed to publicly voice his opposition to
the cabinet’s decisions. As a result, citizens observe the policy outcome but not the
decision process.4 Hence voters are unable to determine who among the coalition
members is responsible when deadlock arises.5
3 For a cross-country study of coalition governments, see Laver and Shepsle (1994) or Muller
and Strom (2000).
4 This is reinforced by the fact that there is rarely any vote in cabinet, implying that no record
of the deliberations is kept.
5 This point is nicely illustrated by Gisela Stuart (MEP) who said about the Council of the
European Union: ”Right now, if my prime minister goes to Brussels and make decisions behind
closed doors, I as a parliamentarian cannot hold him to account because I only know the outcome,
I don’t know the process ... It’s the same with the ministers. They can tell me anything” (New
York Times, 16 June 2003).
2
Based upon those observations, this paper shows that a member of a stable
and ideologically homogeneous coalition who would benefit from a reform may
nonetheless choose to veto its adoption. The argument runs as follows. Consider
a situation where citizens are not perfectly informed about politicians’ preferences
for a reform and where a majority of voters want that reform to be implemented.
One governing party may strategically decide to veto the adoption of the reform
and blame its coalition partners for the deadlock. Citizens then observe the reform
not having been implemented but are unable to determine with certainty where
responsibility lies. The motivation underlying such a strategy is to damage the
reputation some parties have of supporting the reform. By doing so, a party can
increase its chances of being in the next government. This strategy is referred to
as blame-game politics.6
The paper identifies three reasons why a party would want to play the blamegame. The first is related to the issue salience in the electoral debate. A party may
be willing to keep an issue salient (even one on which the party is electorally at a
disadvantage, as we shall see). And one way to do so is by delaying, until after the
next election, the adoption of any reform associated with that issue. The second
reason applies to situations where a politician can hide his stance on an issue. The
third reason concerns a politician who is trying to enhance his bargaining power
in the coalition formation process. This occurs when he can either keep an issue
salient for the other politicians, thus forcing them to take him as a coalition partner
because of his stance on that issue, or get a higher vote share relative to the other
parties, thus increasing its chances of being appointed as the government formateur.
The paper also shows that having a small single-issue party (like the Green
party), in or out of office, does not necessarily help their cause. Indeed that or
another party may want to play the blame-game in order to keep this issue salient
in the next election, or in the formation of the next coalition government.
The remainder of the paper is organized as follows. Section 2 briefly reviews
some related literature. Section 3 outlines the model, and section 4 studies equilibrium policy choices. Section 5 discusses the results, and section 6 concludes.
2. RELATED LITERATURE
This paper is related to the political economy literature on delayed adoption of
socially beneficial reforms. Following Drazen (2000), I classify those models into
three categories. The first strand (often associated with Olson (1982)) considers
policy decisions made by a powerful group who has a vested interest in keeping the
status quo. The second strand is based on the public-good nature of the reform. In
their seminal paper, Alesina and Drazen (1991) consider a war-of-attrition model
where each group waits for the other one to concede and accept to bear a larger
share of the costs associated with the reform. Their argument hinges on asymmetric
information as to how costly the reform is for each group as well as the need for
unanimity to pass the reform. Consensus and uncertainty are also key in our
analysis but, in contrast to theirs, the reform is costless for the governing parties.
The third strand is based on the uncertainty about individual benefits. Laban
and Sturzenegger (1994) show that the adoption of a socially beneficial reform
6 Note that blame-game politics provides a possible explanation for the two examples discussed
above. However it is worth noting that it is not possible to ascertain it is the correct explanation.
Indeed no politician ever claimed having played such a game since that would defeat its most
elementary objective, namely to masquerade.
3
can be delayed by rational voters, despite the fact that economic conditions are
deteriorating over time. This status quo bias relies on ex ante uncertainty about
who will gain and who will lose from the adoption of the reform.7 This contrasts
with the present model where individuals know with certainty whether or not they
will gain from the reform and where there is no such thing as a deterioration of
the status quo over time. Note that a common feature to those three strands is a
conflict of interests, i.e. adopting the reform today instead of tomorrow is (or is
expected to be) harmful for some of the policymakers. Hence, in terms of results,
the present model contrasts with those papers in that it generates delays in the
adoption of reforms that benefit all policymakers (as well as a majority of their
respective electorates), a result we cannot get in those previous contributions.
At a more general level, the current analysis is also related to the literature
on reputational and career concerns initiated by Fama (1980), and formalized by
Holmstrom (1982a). The basic idea is that if an agent’s competence is incompletely
known, the principal can use past outcomes in order to draw some inferences about
the agent’s ability, and then forecast future performances. The agent, being concerned about her future career and anticipating that her current decisions may
signal her competence, then takes actions that will enhance her reputation.
A number of other papers have subsequently looked at situations where those
reputational and career concerns lead to the adoption of inefficient actions. One
strand of this literature considers situations where an agent adopts an inefficient
action in order to preserve or build-up a reputation.8 The present analysis departs
from those models in that the inefficiency comes instead from politicians trying
to damage reputations. Another strand of this literature has focused on situations
where an incumbent manipulates a state variable in an inefficient way so as to make
his fellow politicians less attractive to the voters and thus increase his own probability of reelection.9 While strategic manipulation is also key here, current policy
decisions have an impact on citizens’ voting behavior not only because they affect
constraints on future governments, but also because they provide some information about parties’ policy preferences. Finally, the present analysis is also related
to Holmstrom (1982b) who studies moral hazard in teams. As in this paper, he
shows that in a multi-agent setting, people can cover up improper actions behind
the uncertainty as to who is at fault. However, he also argues that group penalties
are sufficient to discipline agents, a result which no longer holds here.10
This analysis is also related to the literature on sabotage. Lazear (1989) considers a situation where a manager observes each workers’ output and rewards them
on the basis of their relative performance. He shows that such rank-order tournaments discourage cooperation among workers and can then lead to sabotage,
workers taking actions that adversely affect others’ output. Relative performance
7 Their
model is a dynamic version of Fernandez and Rodrik (1991), the latter showing that
uncertainty about the identity of gainers and losers can lead to a socially beneficial reform not being
undertaken, even though it would receive a large political support once introduced. However, while
Fernandez and Rodrik’s model can explain non-adoption of reforms, it cannot generate delays.
Indeed, if the reform is not enacted today, uncertainty about the distribution of gains and losses
still holds and with it the source of the non-adoption. As a result, if the reform is not implemented
today, it will not be implemented tomorrow.
8 See Rogoff and Sibert (1988), Rogoff (1990), Coate and Morris (1995), Holmstrom and Ricart
I Costa (1986), Prendergast and Stole (1996), Morris (2001) and Scharfstein and Stein (1990).
9 See Aghion and Bolton (1990), Milesi-Ferretti and Spolaore (1994) and Besley and Coate
(1998).
1 0 The reason for this difference is that the threat of group penalties is credible in Holmstom
(1982b) but not here.
4
(i.e. parties’ reputations) is also key here. However the relation to this literature
stops here, the present analysis differing in at least two important ways. First,
citizens observe only the ’aggregate outcome’ of the coalition, not the ’output’ of
each party. Second, in terms of outcome, vetoing the adoption of the reform affects
the output of all coalition members, while only the output of the worker who is the
victim of sabotage is affected.
Finally, Groseclose and McCarty (2001) develop a model that has some features
in common with our analysis. In their paper, a one-member Congress submits a bill
to a president who can either sign or veto it. The electorate is uninformed about
the president’s policy preferences but can learn about them from the veto decision.
They show that when the government is divided, the Congress may propose a bill it
knows will be vetoed in order to damage the reputation of the president by making
him appear more extremist than he actually is.11
3. THE MODEL
The model considers a two-period game in which a government has to decide
in each period t ∈ {1, 2} on two issues: the level of public spending and a discrete
reform such as liberalizing trade, building a new road or signing a treaty.12 Let gt ∈
[0, 1] denote the level of public spending in period t and rt the status of the reform,
with rt = 1 (0, resp.) meaning that the reform is (is not, resp.) in effect in period
t. At the beginning of the first period, there is a status quo level of public spending
(e.g. the level implemented by the previous government). A coalition government
has then to decide which level of public spending to adopt and whether to pass the
reform. The decision-making process is sequential, the government first deciding
on the reform issue and then on public spending.13 Each party in the coalition
has veto power and thus, for each issue, a policy different from the status quo is
implemented only if all coalition members agree on it. Citizens observe the policy
outcome p1 = (g1 , r1 ) but not the individual decision of each incumbent. At the
end of the period, an election is held to select a new government and the first-period
1 1 Their analysis differs from the present one in several ways. First, they try to explain the use
of the presidential veto. As a result, they consider a one-period model in a presidential regime.
The current analysis applies rather to coalition governments. Moreover, this paper tries to explain
delays in the adoption of socially beneficial reforms which, by definition, cannot occur in a oneperiod framework. Second, they assume citizens observe the bill that has been submitted and the
president’s veto decision. This leads them to conclude that the decision-making process should
sometimes be kept secret. The present model demonstrates that this may not be true, since the
non-observability of the decision process allows politicians to cover up inefficient actions. Third,
the Congress and the president have heterogenous preferences while here, coalition partners may
share the same preferences for the reform. Finally, only the Congress can play the blame-game
and only citizens’ approval of the president, not of the congressmen, matters. In this paper, all
decision-makers can play the blame-game and all care about their reputation. Hence, politicians
take into account the negative impact of vetoing the adoption of the reform on the reputation of
all parties, including their own.
1 2 The model considers a reform that can be either implemented or rejected. But the same
argument would apply to a continuous policy variable. For example, a party may agree only on
a too moderate fiscal stabilization program and then blame its coalition partners for not having
been able to pass a better one.
1 3 The order in which the government decides on the different issues is not key for the argument;
the same results as those presented below can be obtained (under nearly identical conditions
on incumbents’ preferences) if they first choose the level of public spending and then decide on
the reform issue. In the same time, the government deciding simultaneously on both issues (i.e.
bundling them into an ’omnibus’ bill) is ignored since we want to consider policies which are
important enough that they can become salient in the election.
5
policy becomes the status quo for the second period. If one party gets the majority
of votes in the election, it implements its preferred policy. Otherwise, a coalition
government is formed, in which case unanimity among governing parties is required
for adopting a level of public spending different from g1 and for implementing
(repealing, resp.) the reform had it not been (had it been, resp.) passed in the first
period.
3.1.
Citizens
The polity N consists of a (odd) finite number of citizens N who differ over their
preferences for the two policies. With respect to the reform issue, there are two
preference types, indexed by j ∈ {P, A}, where P (A, resp.) stands for pro-reform
(anti-reform, resp.). Let rj denote the preferred reform outcome of a type-j citizen,
where rj = 1 (0, resp.) if j = P (A, resp.). A citizen of reform type j obtains a
net benefit β j when the reform is in effect, with β P > 0 > β A . With respect to
the public spending issue, each citizen has a unique ideal level g ∈ [0, 1] (though
more than one citizen°can have
type
° the same bliss point). A citizen of spending
°
°
obtains a utility − °g − g ° from a public spending level g, where °g − g ° is
the distance between g and g .14 The utility a type-(
citizen obtains from the
° , j) °
period-t policy pt = (gt , rt ), is then uj (gt , rt ) = − °g − gt ° + β j rt .
Let Nj be the number of reform type-j citizens in the polity and Fj the (discrete)
distribution of spending preference types among the reform type-j citizens. Fj (g)
is thus the number of reform type-j citizens whose preferred level of public spending
lies at or below g. By definition, Nj = Fj (1) and NP + NA = N . Also, let F (g) ≡
FP (g)+FA (g). I assume throughout that NP > NA , i.e. the number of anti-reform
citizens is smaller than the number of pro-reform ones. Hence, implementing the
reform is the outcome preferred by the majority.
3.2.
Parties
Candidates are put forward by three political parties indexed by i ∈ I =
{L, M, R}, where I is the set of parties and L stands for leftist, M for median
and R for rightist. Parties are treated as unitary actors.15 Each party is characterized by its stance on public spending - g i ∈ [0, ¡1] - and on¢ the reform issue j i ∈ {P, A}. Assume g L < g M < g R , and let J ≡ j L , j M , j R denote the profile
of parties’ reform types.
When in office, a politician derives utility from both policies as well as from
ego rents. When not in office, he receives utility only from the policies. In both
cases, politicians discount future utility by a factor δ ∈ (0, 1). The utility a reform
type-j
i derives from the period-t policy pt = (gt , rt ) is uij (gt , rt , m#C ) =
°
° i politician
− °g − gt ° + β j rt + m#C , where m#C denotes the ego rent if the party is in office,
with #C the number of parties in government C, and m#C = 0 if the party is not
1 4 Two things should be noted. First, in order to avoid any confusion with the absolute value
sign |.| I denote Euclidean preferences by k.k. Second, it is worth remarking that the assumption
of Euclidean preferences is not key to the argument. It only allows us to present the results in a
clean and tractable way.
1 5 Considering parties as unitary actors is motivated by the observation that they are traditionally well-disciplined in parliamentary democracies (for a discussion, see Laver and Shepsle
(1994) or Laver and Schofield (1998)). Therefore, I will throughout speak equally of parties and
politicians.
6
in office. I assume m1 > m2 > 0, i.e. the ego rent a party gets decreases with the
number of parties in the government.16
The leftist and median parties are assumed to be in office in the first period
while the rightist party is in the opposition.
3.3.
Information
The distribution of types within the population (i.e. F ) and the position of each
party on the public spending issue (i.e. g i ) are public knowledge.17 However, there
is asymmetric information in that, contrary to politicians, citizens observe neither
the profile of parties’ reform types, nor the policy decision of each coalition partner.
This makes it difficult for them to determine who is responsible for deadlock when
the reform is not adopted in the first period. But citizens can form an initial
estimate of the likelihood that a party is of the pro-reform type (e.g. they might
i
18
observe the roll call over related issues).
Let
³
´ θ ∈ (0, 1) denote such an initial
reputation for party i, with Θ ≡ θL , θM , θR . While parties’ reform types are
observed only by politicians, their initial reputations are common knowledge (e.g.
through newspaper polls).
3.4.
Political Equilibrium
The interaction described above defines a two-period game between citizens and
political parties. The timing of the game is as follows: (1) parties’ reform types are
independently chosen by Nature, and observed solely by politicians; (2) the leftist
and median parties choose the first-period policy p1 = (g1 , r1 ); (3) citizens observe
p1 and cast their ballot for one of the three parties; (4) a second-period government
is formed; and (5) the newly elected government chooses the second-period policy
p2 = (g2 , r2 ). We discuss these stages in reverse order.
Second-Period Policy Choice. Let C2 ⊆ I denote the second-period government.
It has to choose the policy p2 = (g2 , r2 ), first deciding on the reform issue and then
on public spending. For each issue, a governing party proposes a policy outcome.
If all parties in the government propose the same outcome, it is implemented.
Otherwise, the first-period policy remains in place.19 Hence, for each issue, a policy
different from the status quo is implemented only if all the parties in office agree
on it.
1 6 Ego rents are exogenously given and equal for each party in office. However, this assumption
is not restrictive. Indeed, the model can be extended to allow parties to bargain on how to allocate
the spoils of office among the coalition partners. It can also accomodate ego rents which vary with
each party’s vote share (e.g. reflecting the fact that there is traditionally a relation between the
number of cabinet portfolios a party gets and the proportion of its parliamentary seats among the
coalition partners).
1 7 The public knowledge nature of parties’ stance on public spending would apply to issues
with a strong ideological content or to issues which have been the object of a long-standing contention, thus leading to an extensive media coverage (reports, debates, ...). For example, citizens
traditionally know that Democrats prefer spending more on welfare programs than Republicans.
1 8 Note that prior beliefs can also be related to the proportion of pro- and anti-reform agents.
This would follow a citizen-candidate approach where each party selects its candidates among the
citizens who share its preferences for public spending. Priors would then reflect the probability
that party i picks a pro-reform partisan. Our results are consistent with this interpretation.
1 9 This specification of the decision process is meant to capture the unanimity rule discussed
above.
7
Since the second period is the last one, parties have no incentive to make a policy
proposal different from the one they prefer. Two cases are possible, depending on
the type of government. First, suppose a single-party government has been formed.
¡
¢
The ruling party i will then implement its preferred policy, i.e. p2 = g i , ri .
Suppose
government
° has been formed. Let P (C2 , g1 ) ≡
°
°
° a coalition
£ instead
¤ that
{g ∈ g L , g R : − °g k − g ° ≥ − °g k − g1 ° for all k ∈ C2 } be the set of public
spending levels which are (weakly) preferred to g1 by all coalition members.20 The
unanimity requirement implies that the set of equilibrium outcomes is the (nonempty) subset of P (C2 , g1 ) containing all the levels of public spending which are
Pareto optimal for the coalition members. With respect to the reform issue, the
first-period decision will be reversed (i.e. r2 = 1 when r1 = 0 or r2 = 0 when
r1 = 1) only if all coalition parties are of the same reform type (type P for r2 = 1
and type A for r2 = 0). Otherwise, r2 = r1 .
i
Government Formation.
¡ L M RLet
¢ v be the number of votes party i receives in the
election and v ≡ v , v , v
the vector of vote totals. Also denote by WC ≡
ª
©
P
C ⊆ I : k∈C v k ≥ N2+1 the set of possible governments, i.e. those whose vote
for some party i, then that party assumes
total is majoritarian.21 If v i ≥ N+1
2
office alone. If no party receives an overall majority, a coalition government has
to be formed. There are several ways to model the coalition formation process.
I adopt the fixed-order coalition formation procedure due to Austen-Smith and
Banks (1988) where parties are selected as the formateur in a pre-specified order,
the party with the largest vote share first, then the second largest if the first one
fails, and so on (in the event of a tie between several parties, each of them is selected
first with an equal probability).22 The formateur proposes a coalition and parties
then decide whether to accept or reject the formateur’s offer. If it is accepted,
the second-period government is formed. If it is rejected, the party with the next
largest vote share is then asked to form a coalition. And if none of the three parties
manage to form a coalition, a caretaker government assumes office. The first-period
policy then remains in place, and none of the parties receives an ego rent.
A strategy for party i in the coalition formation stage thus consists of two
elements: a proposal and a response strategies. First consider a party i which is proposed to join coalition C. If it accepts, it gets a second-period utility uij (p2 (p1 , C) , m#C ),
where #C is the number of parties in the coalition and p2 (p1 , C) its (correct) beliefs of the policy that government C will implement given the first-period policy
p1 . If party i rejects the offer, it correctly anticipates
C will
¢
¡ ¡ that¢ a government
assume office, and that it will obtain a utility uij p2 p1 , C , m , where m is the
ego rent it gets when C2 = C. Thus party i agrees to join coalition C if and only if
that P (C2 , g1 ) is non-empty since either g1 ∈ P (C2 , g1 ) if g1 ∈ g L , g R or g L ∈
P (C2 , g1 ) (g R , resp.) if g1 < g L (g1 > g R , resp.).
2 1 This excludes the possibility of a minority government, i.e. one which controls less than half
the parliamentary seats. This is motivated by the fact that we consider stable governments (see
Laver and Schofield (1998) for evidence on the lower stability of minority governments).
2 2 The other procedure commonly found in the literature on coalition formation is the probabilistic one due to Baron and Ferejohn (1989), where each party is appointed as the formateur
with a probability proportional to its vote share (for an application of this procedure see for
example Baron and Diermeier (2001)). There is a debate on which of those rules is empirically
relevant. Indeed, while Austen-Smith and Banks (1988) claim that the fixed-order procedure is
a widespread convention, Diermeier and Merlo (2004) find little empirical support for this rule
while the probabilistic one fits the data well. This raises the question of how robust the results
are. In fact, it can be shown that they would also hold under the probabilistic rule (with an extra
requirement on incumbents’ vote shares in proposition 4).
2 0 Note
8
¢ ¢
¡ ¡
uij (p2 (p1 , C) , m#C ) ≥ uij p2 p1 , C , m .
Now consider a formateur party i. It always proposes a coalition C such that i ∈
C. Moreover, since ego rents decrease with the number of parties in the government
and that each party has veto power, it never proposes a consensus government (i.e.
a government that includes all three parties). Now, if party i proposes a coalition
with party k, it gets an expected utility
¡
¢ ¢
¢ ¡ ¡
Uji (p1 , C, J ) = π k uij (p2 (p1 , C) , m2 ) + 1 − π k uij p2 p1 , C , m
, where πk is the probability that party k accepts party i’s offer and C the government which will form following a rejection.
Hence, party i proposes party k that solves
©
ª
max Uji (p1 , {i, k} , J ) | {i, k} ∈ WC .
k6=i
In the event party i is indifferent between forming a coalition with any of the other
two parties, I assume it proposes each with an equal probability.
Election. At the end of the first period, there is an election held under a pure
proportional representation electoral system. Citizens make their voting decision
strategically, anticipating which governments may form and the policies which may
then be enacted in the second period.23 The problem is that citizens do not observe
parties’ reform types, and therefore cannot predict which policy each party will want
to implement and who will take office if a coalition has to be formed. However,
from the first-period policy outcome p1 = (g1 , r1 ) and parties’ initial reputations Θ,
citizens can form beliefs about the profile of parties’ reform types J . Let µi (Θ, p1 )
denote citizens’ posterior beliefs that party i is pro-reform. They are derived from
the priors and incumbents’ first-period strategies through Bayes’ rule whenever
possible and are therefore the same for all citizens in equilibrium.
The voting strategy of a type-( , j) citizen is a function αj which, given her beliefs on parties’ reform types, prescribes for each party i a probability αj (i | Θ, F, p1 )
P
that she votes for party i, with i∈I αj (i | Θ, F, p1 ) = 1. Denote by α the profile
of voting decisions, and let EUj (Θ, p1 , α) be the second-period utility a type-( , j)
citizen expects given the profile of voting decisions α and her beliefs about the
second-period policy outcome.
We can now define a voting equilibrium.
Definition 1. (Voting equilibrium) Given parties’ initial reputations Θ, the
distribution of types within the population F and the first-period policy outcome
p1 = (g1 , r1 ), a strategy profile α∗ (Θ, F, p1 ) is an equilibrium of the voting stage
if and only if for all S ¡⊆ N and for all¢ αS , there exists a citizen in S such that
EUj (Θ, p1 , α∗ ) ≥ EUj Θ, p1 , αS , α−S∗ .
This definition requires the voting equilibrium to be a Strong Nash Equilibrium.
This refinement of the Nash Equilibrium concept imposes stability against deviations not only by individual voters but also by every possible group of voters. The
rationale for imposing such a strong refinement is twofold. First, Nash Equilibrium
is too weak a concept. Indeed, whenever a citizen is not pivotal, the outcome of the
2 3 For
evidence of strategic voting in elections under proportional representation, see Cox (1997).
9
election will be independent of her voting decision, and therefore any strategy will
be a best response to the voting strategies of the other citizens. Second, it allows us
to show that even if citizens can coalesce when making their voting decision, there
still exist equilibria where politicians play the blame-game.
First-Period Policy Choice. The leftist and median parties are in office. They
have to choose the first-period policy p1 = (g1 , r1 ). While the decision process
is the same as in the second period, the policy choice may be different for three
reasons. One is the status quo policy. Denote by p0 = (g0 , r0 ) the policy in place
at the beginning of the first period, and assume that the reform is not in effect (i.e.
r0 = 0). Also consider for simplicity the case where g0 = g M , i.e. the status quo
level of public spending is the one preferred by the median party.24 The second is
that parties have reputational concerns. Indeed, voters use the first-period policy
outcome in order to draw some inferences about the reform types of the incumbents.
Hence, coalition members improve their reputation as supporters of the reform by
implementing it in the first period. Citizens also realize that the reform type of
the rightist party may influence incumbents’ first-period policy decisions, and thus
use this information to update their beliefs about the reform type of the rightist
party. The third difference is that the policy adopted in the first period becomes
the status quo for the second period. And this status quo may determine who will
assume office in the second period in the event a coalition government has to be
formed. Incumbents take this into account when making
their
¡
¢ policy decision.
An incumbent i’s first-period strategy is a pair σ i1 , γ i1 which consists of reform and public spending strategies. The reform strategy is a function σ i1 , where
σ i1 (Θ, J , F, p0 ) is the probability that incumbent i adopts the reform. This depends on the status quo policy p0 , on the level of public spending he expects to
be implemented after the reform choice, on his anticipation of citizens’ voting decisions (which depend on parties’ initial reputations Θ, the distribution of types
within the population F and the first-period policy outcome p1 ) and of the government which will form and the policy implemented in the second period (which
depend on the first-period policy outcome, the election outcome and the profile of
parties’ reform types J ). Similarly, a public spending strategy for incumbent i is a
function γ i1 , where γ i1 (Θ, J , F, p0 , r1 ) is party i’s proposed level of public spending
which also depends on the first-period reform decision r1 .25 Denote by Vji (p1 ) the
second-period expected utility of a reform type-j party i when the first-period policy is p1 . An incumbent i chooses his first-period strategy to maximize his expected
2 4 This assumption is made to simplify the analysis. An incumbent’s incentives to play the blamegame are different for a different g0 . For some values, an incumbent might rely upon the public
spending issue to prevent its coalition partner from playing the blame-game. For other values, it
might provide an incumbent with the incentive to play the blame-game, incentive he would not
have had otherwise. However, presenting the results for each g0 would not only be tedious but
would also significantly complicate the analysis without adding much to our understanding of the
argument, the basic intuition remaining unchanged. It seems therefore reasonable to consider a
specific level of the status quo. Now letting g0 = g M is a natural choice given that g M corresponds
to what can be interpreted as the long-run or stable level of public spending (for a discussion of
this point, see Austen-Smith (2000) whose argument, although developed in a slightly different
framework, applies to the present model. See also Baron (1996)).
2 5 In order to simplify the notation, I will throughout omit Θ, F and p from the arguments of
0
σ i1 and γ i1 .
10
intertemporal payoff, i.e.
⎧ i
ª
©
max uij (p1 (σ1 ) , m2 ) + δ Vji (p1 (σ 1 )) , and
⎪
⎨ σ 1 (J ) ∈ arg
i
σ 1 ∈[0,1]
ª
©
i
γ
(J
,
r
)
∈ arg max uij (g1 (γ 1 ) , r1 , m2 ) + δ Vji (g1 (γ 1 ) , r1 )
⎪
1
1
⎩
i
γ 1 ∈[0,1]
¢
¢
¡
¡
M
M
, where σ 1 = σL
and γ 1 = γ L
1 , σ1
1 , γ1 .
Finally, note that each party deciding with probability one not to implement the
reform in the first period or to keep the status quo level of public spending is always
an equilibrium. To see this, recall that both parties must agree to the reform or to
a level of public spending different from g0 . Hence, if the other coalition member
does not adopt the reform or proposes g0 , acting differently does not change the
policy outcome. As a result, neither party has an incentive to deviate. However,
there are situations where both incumbents would be better off implementing the
reform or a level of public spending different from the status quo. In those cases,
such equilibria require a coordination failure. But this does not seem realistic in
this game. I thus disregard those coordination failures by assuming that incumbents’ strategies are weakly undominated (i.e. incumbents choose their first-period
strategy conditional on being pivotal).
Political Equilibrium. A Perfect Bayesian Equilibrium of this game consists of:
(i) first-period policy choice strategies for both the leftist and median parties; (ii)
a voting strategy for each citizen; (iii) government formation strategies for each
party; (iv) second-period policy choice strategies for each party; and (v) voters’
beliefs concerning the reform type of each party.26 These must satisfy the following requirements. First, strategies for the leftist and median parties (government
formation as well as first- and second-period policy choice strategies) must be optimal given other parties’ strategies and citizens’ strategies and beliefs. Second,
strategies for the rightist party (government formation and second-period policy
choice strategies) must be optimal given other parties’ strategies. Third, citizens’
posterior beliefs are derived from incumbents’ strategies through Bayes’ rule where
possible. Finally, a citizen’s strategy (a voting rule) must be optimal given her
beliefs and parties’ strategies.
4. BLAME-GAME POLITICAL EQUILIBRIA
We now investigate the existence of blame-game political equilibria. A proreform party is said to play the blame-game if it vetoes the adoption of the reform
and takes advantage of the voters’ inability to determine where responsibility for the
policy outcome lies. A blame-game equilibrium is then defined as an equilibrium in
which some parties play the blame-game. It is worth noting that this may happen
only in the first period. Indeed, the second period being the last one, parties have
at that time no reputational concerns and thus no incentive to propose a reform
outcome different from the one they prefer.
Throughout the analysis, I will maintain the following technical assumption:
³ R L
´
¡
¢
R
M
δ
Assumption 1 (i) |β A | ≥ 1−δ
m1 + g M − g L ; and (ii) θR ∈ g β−g , 1 − g β−g .
P
2 6 Note
P
that the equilibrium concept used here is actually stronger than Perfect Bayesian Equilibrium since the voting equilibrium has to be a Strong Nash Equilibrium.
11
Part (i) guarantees that an anti-reform party will never want to implement the reform. This assumption is made to be consistent with the idea that an incumbent
plays the blame-game in order to damage the reputation of its coalition partner
by letting the voters believe that the latter is of the anti-reform type and thus is
the one who vetoed the adoption of the reform.27 Part (ii) puts lower and upper
bounds on the initial reputation of the rightist party. Note that while being sufficient for the characterization of blame-game political equilibria, assumption 1 is in
most cases much stronger than necessary.
The analysis that follows will
¡ focus¢ on political equilibria where the first-period
policy outcome is always p1 = g M , 0 , i.e. the reform is not implemented and the
level of public spending is the one preferred by the median party. This means that
citizens obtain no information
¡ from the
¢ first-period policy outcome and therefore
that Bayes’ rule implies µi Θ, g M , 0 = θi for all i ∈ I, i.e. citizens’ posterior
beliefs on parties’ reform types coincide with their priors. However, the definition
of a Perfect Bayesian Equilibrium does not put any restriction on beliefs
³ off the
´
equilibrium path. For simplicity, I adopt the following ones: µ (Θ, g, 1) = 1, 1, θR
³
´
for all g and µ (Θ, g, 0) = 0, 0, θR for g 6= g M , where the first entry (second and
third, resp.) corresponds to the posterior beliefs that the leftist party (median and
rightist, resp.) is pro-reform.28 It is worth emphasizing that those are not the only
beliefs that support the equilibrium outcomes presented below. Moreover, they
satisfy Cho and Kreps’ (1987) Intuitive Criterion.29
The following sub-sections identify each a different motivation for a politician
to play the blame-game.
4.1.
Issue salience in the electoral debate
The first two propositions show an incumbent who is willing to play the blamegame in order to keep the reform issue salient in the electoral debate.
2 7 There is another reason for considering only equilibria where an anti-reform politician always
vetoes the adoption of the reform. Situations where an agent has preferences opposed to those
of a principal and yet decides to conform in order to enhance his reputation, have already been
studied (see for example Barro (1973), Ferejohn (1986) or Austen-Smith and Banks (1989) for
agency style models of political competition where elections give politicians the incentive to make
decisions in accordance with the desires of their constituents). Instead I will focus on situations
where the principal (viz. the majority of voters) and the agent (viz. incumbents) have the same
preferences but the agent nevertheless decides not to adopt the policy they both desire.
2 8 Note that if the incumbents anticipate that a coalition government will have to be formed in
the second period, they might want to implement a level of public spending different from g M .
Suppose for instance that the rightist party will be the first to be appointed as the formateur and
that it is indifferent between forming a coalition government with any of the other parties. It will
then propose each of them with an equal
Anticipating that both will accept the offer,
probability.
incumbents may then agree on g1 = g M + ε for ε > 0 arbitrarily small. They will now have
an incentive to reject the rightist party’s offer and wait for one of them to be appointed as the
formateur. This incentive comes from the fact that the rightist party will veto any g2 < g1 while
by renewing the coalition, incumbents will be able to implement a level of public spending they
both prefer, e.g. g2 = g M . Hence, by losing ε in the first
period,
they increase their probability
of staying in office from one half to one. µ (Θ, g, 0) = 0, 0, θR for g 6= g M allows us to rule out
this possibility and therefore to concentrate on blame-game strategies, the focus of the paper.
2 9 Since an anti-reform party always vetoes the adoption of the reform (by assumption 1(i)) and
because of the unanimity rule, the reform is implemented only if both incumbents are of the proreform type. Thus µ (Θ, g, 1). In the same time, equilibrium dominance does not eliminate any
reform type following a first-period policy outcome p1 = (g, 0), g 6= g M , given that they might all
prefer to propose a level of public spending g 6= gM if they would then get the absolute majority
in the next election.
12
h ³
´ ³
´
i
Let e
θ ≡ θL θM + θR θL 1 − θM + 1 − θL θM be the initial beliefs that at
least two parties are pro-reform. We have the following result.
Proposition 1. Suppose assumption 1 is satisfied. There exist θ ∈ (0, 1) and
distributions of preference types within the population (F ) such that there is a political equilibrium in which a pro-reform leftist incumbent always vetoes the adoption
of the reform in the first period in order to get the votes of all pro-reform citizens if his initial reputation exceeds θ and the following two conditions hold: (i)
o β − gR −gL
n
¡
¢
(
)
θ < P
; and (ii) δ (m1 − m2 ) ≥ β + g M − g L .
max θM , θR , e
P
βP
The proof of this and all subsequent results are reported in the Appendix.30
Condition (i) puts an upper-bound on the priors, thus ensuring θ < 1.31 Condition (ii) says that a pro-reform incumbent is more office than policy motivated
in the sense that the present value of the utility gain from getting the absolute
majority tomorrow exceeds the gain from having his preferred policy implemented
in the first period.
The intuition underlying this result runs as follows. Consider a first-period
coalition where both incumbents are pro-reform.32 Also suppose without loss of
generality that the median party proposes to adopt the reform, and thus that
party L’s first-period reform decision is pivotal. A pro-reform leftist party knows
that if the reform is implemented in the first period, citizens will infer that both
incumbents are of type P. This comes from the fact that an anti-reform politician
prefers the status quo and that both incumbents must agree for the reform to
pass. Now, if the leftist party anticipates it will not get the absolute majority, it
may decide to veto the adoption of the reform. And given that incumbents have no
electoral
to agree on a level of public spending different from g M , we have
¡ Madvantage
¢
p1 = g , 0 for any profile of incumbents’ reform-preference types, and citizens
do not get any information on parties’ reform types. In other words, while voters
observe that the reform is not enacted, they are not sure whether it comes from
a type-P party L playing the blame-game or from an anti-reform incumbent who
implements his preferred reform outcome. Because of his high initial reputation
as supporter of the reform (θL > θ), the leftist incumbent will then get all the
pro-reform votes and thus the absolute majority.33 Hence, proposition 1 shows
a pro-reform politician who plays the blame-game in order to gain the absolute
majority in the next election by taking advantage of his reputation on that issue.
This result is consistent with the observation that coalition governments tend to
respond slowly to unexpected fiscal deficits. But contrary to the previous literature,
it does not require heterogeneous policy preferences among coalition members in
order to explain this observation. To illustrate this, consider a coalition government
made up of a left-wing and a right-wing party. During their term in office, a shock
arises that requires the adoption of a stabilization program. Both parties as well as
a majority of the electorate are in favor of such a program. Parties know that if it is
implemented neither of them will get the majority in the next election. Hence, the
3 0 The
conditions on the distribution of preference types (F ) are formally stated there as well.
R
L
β −(g R −g L )
that P β
> 0 follows from 1 > θR > g β−g (by assumption 1(ii)).
P
P
3 2 It is worth mentioning that although we discuss only the case of a pro-reform coalition (since
the focus of the paper is on a pro-reform party playing the blame-game), all the results and proofs
are established for any profile of parties’ reform types.
3 3 One may wonder how restrictive θ L > θ is. To give just an example, suppose g L = 1/3,
g R = 2/3, β P = 4/3, θM = 1/2 and θR = 1/4. Then this condition requires θL > 3/4.
3 1 Note
13
right-wing members of the cabinet may decide to block the adoption of this fiscal
stabilization program, taking advantage of their reputation as being fiscally tough,
and blame the left-wing party for the deadlock. Pro-reform citizens will then bias
their vote towards the right-wing party since it appears to be more likely than the
leftist to implement the program.
Playing the blame-game can be interpreted here as a way to make the reform
the campaign issue of the next election. Indeed, if the reform is implemented in
the first period, citizens will infer that both coalition parties are pro-reform. The
salient issue for the swing voter then shifts from the reform to public spending. The
problem is that the leftist party has no particular advantage on this latter issue.
Instead, if party L plays the blame-game, the question of which parties are of type
P remains, and with it the focus of the election campaign on the reform issue. And
here the leftist party can benefit from its reputational advantage. By his policy
choice, an incumbent can thus focus the election campaign on some specific issues,
thereby eliminating candidates who can prevent him from winning the election.
This provides a possible explanation for the strategy followed by Jacques Chirac
during the 2002 Presidential election campaign in France, where he blamed Jospin
for the non-adoption of homeland security reforms.34 Chirac, having a better reputation as a supporter of a tight security policy than Jospin, may have strategically
chosen to delay the adoption of those reforms knowing that Jospin was weaker on
that issue and thus could be defeated if this issue becomes salient in the presidential
election.
In the above proposition, a politician plays the blame-game in order to get the
absolute majority in the next election. And he does so by taking advantage of his
reputation as a supporter of the reform. The next result shows that a politician
may also play the blame-game in order not to attract votes but to split another
candidate’s electorate by taking advantage of that candidate’s reputation being
relatively low and not necessarily of his own being high.
h ´
Proposition 2. Suppose assumption 1 is satisfied. There exist θ ∈ 0, e
θ and
distributions of preference types within the population (F ) such that there is a political equilibrium in which a pro-reform leftist incumbent always vetoes the adoption of
the reform in the first period in order to deprive his coalition partner from getting the
majority of votes in the next election if the initial reputations of ³
the leftist
´ andgiright| −gM |
i
ist parties exceed θ and the following two conditions hold: (i) θ − e
θ < β
P
¢
¡
for all i ∈ I; and (ii) δ m22 ≥ β P + g M − g L .
As in proposition 1, condition (i) puts an upper-bound on the initial reputations. Condition (ii) says that for a pro-reform incumbent the present value of the
expected utility gain from being in office tomorrow exceeds the utility gain from
having his preferred policy implemented today.
The logic underlying this result runs as follows. Consider again a pro-reform
coalition where the median party proposes to adopt the reform. If the reform is
implemented in the first period, citizens will infer that both incumbents are of type
P and, given its stance on the public spending issue, the median party will get a
majority of votes. The leftist party may then choose to veto the adoption of the
3 4 It is worth remarking that French Presidential elections are held under plurality runoff, not
proportional representation. However, the argument developed here can be extended to this
electoral system.
14
reform, thereby depriving the voters from the assurance that party M is of the proreform type. But if the reform issue is salient for some of the pro-reform citizens who
would have voted for the median party had the reform been implemented and the
reputation of this party is relatively low (i.e. θM < e
θ, which follows from condition
(i)), those citizens will prefer to cast their ballot for another party. Hence they
swing the election by depriving the median party from the absolute majority. In
other words, by playing the blame-game, the leftist incumbent makes the reform the
salient issue in the election. Now if neither party gets the absolute majority in the
election, a coalition has to be formed. Since the median incumbent had no electoral
advantage to agree on a level of public spending different from his preferred one,
g1 = g M and therefore any coalition government will implement g2 = g M as well.
Suppose now that the rightist party is of the anti-reform type. Since it would have
the power to veto the adoption of the reform in the second period (and it would
definitely use that power), the incumbents are better off renewing the first-period
coalition (eventually rejecting an offer to join the rightist party in a coalition in the
event this party is the first to be appointed as the formateur). Instead, if the rightist
party is also of the pro-reform type, then any coalition will implement the reform,
and the second-period government will consist of the party which is first appointed
as the formateur and each of the other two parties with an equal probability. To
sum up, party L plays here the blame-game in order to prevent its coalition partner
from getting the absolute majority in the next election, thereby making possible its
participation in a second-period coalition. It does so by keeping the reform issue
salient in the electoral debate thus taking advantage of its coalition partner having
a relatively low reputation as a supporter of the reform.
To appreciate this argument, consider a coalition government composed of the
Democratic and Green parties. The government has to decide whether to ban
night flights at an airport. The Democratic party appears less likely to support
this ban since some of its partisans are employed at the airport. But night flights
are disturbing for the neighborhood and the environment, thus making the ban
appealing for the Green party and the issue salient for people living close to the
airport. Hence, those citizens will vote for parties which are likely to support the
ban. Despite its preferences and the fact that the Democrats want to adopt the
ban, the Green party may decide to reject it, and shift the responsibility onto the
Democratic party.
This result contrasts with the previous one in two ways. First, the leftist party
plays the blame-game in order to prevent its coalition partner from getting the
absolute majority and not, as in proposition 1, to guarantee itself the majority.
Second, the leftist party no longer relies solely on its reputation. It may even be
the one among the three parties which is perceived by the voters as the least likely
to support the adoption of the reform. In that case, it will have to rely on a higher
reputation of the opposition party for splitting the electorate of its coalition partner.
One example of this would be a left-wing party blocking immigration reforms and
blaming its right-wing coalition partner for it. Its objective would be to weaken the
electoral position of its coalition partner by inducing some of the latter’s supporters
to switch their vote to an extreme rightist party.
4.2.
Divided electorate
The second motivation applies when an incumbent tries to hide his preference
for the reform in order to avoid a split in his electorate that would cost him his
15
anti-reform votes.
Proposition 3. Suppose assumption 1 is satisfied. There exist distributions of
preference types within the population (F ) as well as θ and θ (with 0 ≤ θ < θ ≤ 1)
such that there is a political equilibrium where a pro-reform leftist party whose
initial reputation lies between θ and θ always vetoes the adoption of the reform in
the first period in order to hide its stance on the reform, provided the following two
M
L
max{θM ,θ R ,h
θ}−min{θM ,θ R ,h
θ}
< g |β−g| ; and (ii) δ (m1 − m2 ) ≥
conditions hold: (i)
2
A
¡
¢
β P + gM − gL .
This proposition tells us that an incumbent may play the blame-game because
of the heterogeneity in his electorate’s attitude towards the reform.35 To see this,
suppose that the leftist electorate is majoritarian with a large fraction being of the
anti-reform type. If the reform is implemented in the first period, citizens will infer
that both incumbents are of type P. Anti-reform voters may then prefer casting
their ballot for the opposition party if its initial reputation is low enough. This will
deprive party L from the absolute majority it would have gotten had it obtained the
votes of all the leftist citizens (pro- and anti-reform ones). Party L may then decide
to veto the adoption of the reform. The first-period decision will thus convey no
information about the reform types of the different parties and party L’s reputation
will now be closer to or lower than the opposition party’s. This will then strip the
leftist anti-reform citizens from the incentive they had to vote for party R. If in the
same time party L’s initial reputation is not too low such that the leftist pro-reform
citizens have no incentive to vote for another party, party L will then obtain the
leftist votes and thus the majority. By his policy choice, an incumbent can thus
hide his stance on a specific issue and avoid a split in his electorate.
To illustrate this proposition, consider a coalition government consisting of the
Democratic and Republican parties. This government has to decide whether to
sign an environmental treaty. Opinions are divided. If the treaty is signed, the
Conservatives will lose the support of a large fraction of their electorate who opposes
it. Hence, the Conservative party may block the adoption of the treaty in order
to satisfy its anti-reform members while at the same time letting its pro-reform
members believe that the veto came from the Democratic party.
4.3.
Bargaining power in the coalition formation
The last motivation applies to an incumbent who tries to enhance his bargaining
power in the coalition formation process through one of the following channels. The
first one is by increasing his vote share relative to the other parties in such a way
that he is the first to be appointed as the formateur. The second one is by making
the reform the salient issue in the coalition bargaining in order to take advantage
of his stance on that issue.
h ´
Proposition 4. Suppose assumption 1 is satisfied. There exist θ ∈ 0, e
θ and
distributions of preference types within the population (F ) such that there is a political equilibrium in which a pro-reform incumbent vetoes the adoption of the reform
3 5 Note that condition (i) puts here an upper-bound on how large the range of initial reputations
can be, while condition (ii) just repeats condition (ii) from proposition 1.
16
in the first period in order to guarantee his participation in the second-period coalition government by enhancing his bargaining power, if the initial reputations of the
leftist and rightist parties exceed θ and the same two conditions as in proposition 2
hold.
To understand the intuition behind proposition 4, consider as before a proreform coalition. But suppose now that neither party gets a majority of votes when
the reform is implemented in the first period. Moreover assume for instance that
the rightist party gets the largest vote total among the three parties. It will then
be appointed as the formateur and propose a coalition with one of the incumbents,
say the median party. Anticipating that his coalition partner will accept this offer,
the leftist incumbent may decide to veto the adoption of the reform in the first
period in order to prevent this from happening. Now two cases are possible.
First, suppose the rightist party is of the pro-reform type. The leftist incumbent
will have an incentive to veto the adoption of the reform if by doing so it gets the
largest vote share, thus being the first one to be asked to form the second-period
government. Hence, an incumbent plays here the blame-game in order to increase
his bargaining power in the coalition formation by being the one who is appointed
first as the formateur.
Consider now the case where the rightist party is of the anti-reform type. The
key to the argument here is that the reform issue will not be salient in the coalition
formation bargaining if it is implemented in the first period. Indeed, any coalition
government will keep the reform in place in the second period since at least one of
the incumbents will be in office and will thus be able to veto a repeal of the reform.
Instead if the reform is not adopted in the first period, it will be the salient issue
in the coalition bargaining since only a pro-reform coalition will implement it in
the second period. This will provide the leftist party with an incentive to play the
blame-game. Indeed, if the median party accepts party R’s offer, it knows that the
latter will veto the adoption of the reform in the second period. The median party
will thus prefer to reject the offer and instead share office with the pro-reform leftist
party. Hence, as in propositions 1 and 2 this result shows an incumbent who plays
the blame-game in order to keep an issue salient. But the target differs. Before it
was aimed at the citizens whose change in their voting behavior was either giving
the blame-game player the absolute majority in the election or depriving another
party of the majority. Here it is directed towards the politicians whose change in
their coalition formation behavior guarantees the blame-game player a seat in the
second-period government.
5. DISCUSSION
There is no real puzzle to the non-adoption of a reform by a minority whose
interests differ from the remaining of the population and who would be hurt by
its implementation. Decision-makers then act in their best interest. In the present
model this happens when at least one of the governing parties is of the anti-reform
type. What is more surprising is when the reform is rejected by a majority who
would have been better off carrying it out. This occurs when the veto comes from a
member of a pro-reform coalition. But then, in any of the above results, the reform
is implemented in the second period. Hence, the model provides an explanation for
why the adoption of a (welfare-enhancing) reform preferred by all the members of a
17
coalition government as well as a majority of the electorate is sometimes delayed.36
While this model analyzes the case of a coalition government, its logic can be
applied to many political systems where the government is divided. The French
cohabitation between 1986 and 1988, where the executive was divided between a
socialist president and a conservative cabinet, is a good illustration. During the
1988 presidential election campaign, incumbent President Mitterand and Prime
Minister Chirac (the two major candidates in that election) blamed each other for
having blocked the adoption of some reforms. The 1997-2002 cohabitation between
President Chirac (Conservative) and Prime Minister Jospin (Socialist) is another
good example. As I previously mentioned, during the 2002 presidential election
campaign, Chirac who was running against Jospin blamed him for a lax attitude
towards security, thus exploiting his better reputation as a supporter of a stringent
security policy.
The model can also be applied to more general situations where several agents,
having some private information, choose an action while the principal observes only
the aggregate outcome. Consider first the example of a negotiation between a trade
union and the management of a firm. An agreement satisfying both parties may
be rejected by one of them in order to spoil the reputation of the other and obtain
public support. The argument also applies to sports teams. Consider a football
team that has just appointed a new coach who is disliked by the players. Some of
them may then decide to play badly and blame this new coach for the team’s poor
results, hoping he will be laid off. Finally, consider a firm that has just hired a
new manager. Then some of the incumbent managers, fearing that he will get the
promotion they were expecting, may sabotage several projects and put the blame
on him. What these examples all have in common is the principal’s inability of
determining where the responsibility for the currently bad results lies.
Finally, this model also shows that having a small party advocating a specific
issue (the Green party, for instance) does not necessarily help their cause. Indeed,
those parties often have a small electorate and therefore no hope of getting the
absolute majority. In addition, citizens perceive them as the most likely to support
the issue they champion. Thus, proposition 2 shows that if their policy motivation is
not too strong, those small governing parties may have an incentive to block reforms
they favor in order to prevent other parties from getting the absolute majority,
which may thus allow them to stay in office. And proposition 4 demonstrates that
they may also want to keep salient the issue they champion, thus preserving in the
coalition formation process the advantage they derive from their policy stance. In
fact, this argument holds even if they are not in the government. Indeed, some of
the major governing parties may use the policy concerns of those small parties as
a ’battlefield’ during the election campaign - as Chirac may have done with the
security policy, an issue championed by Le Pen’s National Front party.37
3 6 It
is worth noting that in this model only delayed adoption can occur if all coalition members
are pro-reform. However failure to implement such reforms can happen if some cabinet members
are anti-reform.
3 7 We can illustrate this argument using the example of social security reforms. The aging of
the population in Western democracies requires an adjustment of social security programs. In
some countries an elderly-people party has been formed. One might think that this will increase
pressure on governing parties to adopt a reform. Our results suggest, however, that it is not
necessarily the case. Let’s first consider a situation where the elderly-people party is not in office.
If the government is divided between two parties, say the Democratic and Republican parties,
the former may want to veto such a reform. By doing so, it will strengthen the electorate’s
awareness of the necessity for such a reform and thereby weaken the Republican party which
18
6. CONCLUSION
Most of the models that try to explain delays in the adoption of reforms do
so in the context of a single-party government. In this paper I propose a model
where the government is a coalition. The model takes into account two features
of coalition governments, namely that decisions have to be unanimous and that
cabinet members are collectively responsible for the decisions made. The paper
then shows that those features create a rationale for delaying the adoption of a
reform - that I call blame-game -, namely damaging the reputation of coalition
partners (including his own) in order to improve one’s electoral prospects relative
to others’. The model shows that this can happen in a stable coalition government
where all its members favor the reform, the citizens are rational and cooperate when
making their voting decisions, and a majority of the electorate wants the reform to
be passed.
The paper then goes on identifying three motivations for a coalition member
to play such a game. A first motivation is to keep an issue salient in the next
election. And this motivation may arise even if the coalition member is electorally
at a disadvantage on that issue, provided that it is going to hurt others as well. A
second motivation is to hide one’s stance on an issue in order to prevent a split in
one’s electorate during the next election. A third motivation is to improve one’s
bargaining power in the formation of the next coalition government.
Hence the model predicts that we can expect delays in the adoption of a reform
if one coalition member is sufficiently office-motivated and: (1) has either a high
reputation on that issue, or an intermediate one with an electorate which is divided
on that issue; (2) has a coalition partner with a relatively low reputation on this
reform issue but an electoral advantage on another; or (3) who faces the risk of not
being invited to join the next coalition government.
Finally the paper argues that having a small single-issue party may hurt the
cause they champion. Indeed that or another party may want to play the blamegame in order to keep this issue salient in the next election, or in the formation of
the next coalition government.
REFERENCES
[1] Aghion, Ph. and P. Bolton, 1990. Government domestic debt and the risk of
default: a political-economic model of the strategic role of debt. In: Public
Debt Management: Theory and History, Dornbusch, R. and M. Draghi (eds),
Cambridge University Press, Cambridge, 315-345.
[2] Alesina, A. and A. Drazen, 1991. Why are stabilizations delayed?. American
Economic Review 81, 1170-1188.
traditionally exhibits less interest in those welfare programs. The electoral race will then shift
from Democratic vs. Republican to Democratic vs. elderly-people party. But the latter party,
not having a well-defined program on other issues, will be defeated by the Democrats who will
win the majority. Let’s now consider the case where the elderly-people party is in office. If the
government is divided between the Democratic party and the elderly-people party, the latter may
want to play the blame-game. By doing so, it may prevent the Democratic party from getting
the majority and thus may guarantee itself a participation in the next cabinet. Or, it may leave
to the next government the decision to reform the social security system. Now if the Democrats
want this reform to pass, they may have no other choice than renewing the coalition with the
elderly-people party.
19
[3] Austen-Smith, D., 2000. Redistributing income under Proportional Representation. Journal of Political Economy 108, 1235-1269.
[4] Austen-Smith, D. and J. Banks, 1988. Elections, coalitions, and legislative
outcomes. American Political Science Review 82, 405-422.
[5] Austen-Smith, D. and J. Banks, 1989. Electoral accountability and incumbency. In: Models of Strategic Choice in Politics, P. Ordeshook (ed.), University of Michigan Press, Ann Arbor, MI.
[6] Baron, D., 1996. A dynamic theory of collective goods programs. American
Political Science Review 90, 316-330.
[7] Baron, D. and D. Diermeier, 2001. Elections, governments, and parliaments
in Proportional Representation systems. Quarterly Journal of Economics 116,
933-967.
[8] Baron, D. and J. Ferejohn, 1989. Bargaining in legislatures. American Political
Science Review 83, 1181-1206.
[9] Barro, R., 1973. The control of politicians: an economic model. Public Choice
14, 19-42.
[10] Besley, T. and S. Coate, 1998. Sources of inefficiency in a representative democracy: a dynamic analysis. American Economic Review 88, 139-156.
[11] Cho, I. and D. Kreps, 1987. Signalling games and stable equilibria. Quarterly
Journal of Economics 102, 179-221.
[12] Coate, S. and S. Morris, 1995. On the form of transfers to special interests.
Journal of Political Economy 103, 1210-1235.
[13] Cox, G., 1997. Making Votes Count. Cambridge University Press, Cambridge.
[14] Diermeier, D. and A. Merlo, 2004. An empirical investigation of coalitional
bargaining procedures. Journal of Public Economics 88, 783-797.
[15] Drazen, A., 2000. Political Economy in Macroeconomics. Princeton University
Press, Princeton, NJ.
[16] Fama, E., 1980. Agency problems and the theory of the firm. Journal of Political Economy 88, 288-307.
[17] Ferejohn, J., 1986. Incumbent performance and electoral control. Public Choice
50, 5-25.
[18] Fernandez, R. and D. Rodrik, 1991. Resistance to reform: Status quo bias in
the presence of individual-specific uncertainty. American Economic Review 81,
1146-1155.
[19] Grilli, V., D. Masciandaro and G. Tabellini, 1991. Political and monetary
institutions and public financial policies in the industrial countries. Economic
Policy 13, 341-392.
[20] Groseclose, T. and N. McCarty, 2001. The politics of blame: bargaining before
an audience. American Journal of Political Science 45, 100-119.
20
[21] Holmstrom, B., 1982a. Managerial incentive problems: a dynamic perspective. In: Essays in Economics and Management in Honor of Lars Wahlbeck.
Helsinki: Swedish School of Economics.
[22] Holmstrom, B., 1982b. Moral hazard in teams. The Bell Journal of Economics
13, 324-340.
[23] Holmstrom, B. and J. Ricart I Costa, 1986. Managerial incentives and capital
management. Quarterly Journal of Economics 101, 835-860.
[24] Laban, R. and F. Sturzenegger, 1994. Distributional conflict, financial adaptations and delayed stabilizations. Economics and Politics 6, 257-276.
[25] Laver, M. and N. Schofield, 1998. Multiparty Government. The Politics of
Coalition in Europe. University of Michigan Press, Ann Arbor, MI.
[26] Laver, M. and K.A. Shepsle (eds), 1994. Cabinet Ministers and Parliamentary
Government. Cambridge University Press, Cambridge.
[27] Lazear, E., 1989. Pay equality and industrial politics. Journal of Political Economy 97, 561-580.
[28] Milesi-Ferretti, G.M. and E. Spolaore, 1994. How cynical can an incumbent
be? Strategic policy in a model of government spending. Journal of Public
Economics 55, 121-140.
[29] Morris, S., 2001. Political correctness. Journal of Political Economy 109, 231265.
[30] Muller, W. and K. Strom (eds), 2000. Coalition Governments in Western Europe. Oxford University Press, Oxford.
[31] Olson, M., 1982. The Rise and Decline of Nations. Yale University Press, New
Haven, CT.
[32] Prendergast, C. and L. Stole, 1996. Impetuous youngsters and jaded old-timers:
acquiring a reputation for learning. Journal of Political Economy 104, 11051134.
[33] Rogoff, K., 1990. Equilibrium political budget cycles. American Economic Review 80, 21-36.
[34] Rogoff, K. and A. Sibert, 1988. Elections and macroeconomic policy cycles.
Review of Economic Studies 55, 1-16.
[35] Roubini, N. and J. Sachs, 1989. Political and economic determinants of budget
deficits in the industrial democracies. European Economic Review 33, 903-938.
[36] Scharfstein, D. and J. Stein, 1990. Herd behavior and investment. American
Economic Review 80, 465-479.
21
7. APPENDIX
Let’s first introduce some extra notation. Let v i (g1 , r1 ) be party
¡ ¢ i’s vote total
given the first-period policy outcome p1 = (g1 , r1 ). Also let σ i2 j i be the probability that in the second period party i proposes the reform to be in place, and
γ i2 (C2 , g1 ) be the level of public spending party i proposes in the second period when
the government is C2 and the status quo level of public spending g1 . Also whenever
it is possible to do so without causing a confusion, I shall denote the voting strategy
and period-t utility of citizen n as αn (.; p1 ) and un (pt ), respectively.
I now state and prove two additional lemmas which will be used in the proofs
of the propositions stated above.
¡
¢
Lemma 1. If v i g M¡, r1 <¢ N+1
2 ©for all i ∈ I, ªthen the unique¡second-period
¢
policy outcome is p2 = g M , 1 if # i ∈ I : j i = P ≥ 2 and p2 = g M , 0 otherwise.
Proof. I prove the result
via
¡
¢ the following three claims.
¡
¢
Claim 1 Suppose p1 =¡ g M , 0¢ and #C2 ≥ 2. Then p2 = g M , 1 if j i = P for all
i ∈ C2 , otherwise p2 = g M , 0 .
Proof of Claim 1. Since the second period is the last one, neither party has
a reputational
incentive to propose a reform outcome different from its ideal one,
¡ ¢
i.e. σi2 j i = ri for all i ∈ I. Given that r1 = 0, r2 = 1 only if all second-period
coalition members choose to adopt the reform. This occurs only if j i = P for all
i ∈ C2 . Otherwise, r2 = 0.
¡
¢ © ª
That g2 = g M follows
from¢ P C2 , g M = g M for all¡C2 ⊆ I¢ with #C2 ≥ 2. ¥
¡ M
M
Claim 2 Suppose p1 = g , 1 and
¡ M #C¢2 ≥ 2. Then p2 = g , 1 if there exists i ∈
i
C2 with j = P , otherwise p2 = g , 0 .
Proof of Claim ¡2. Obvious.
¥
¢
N +1
i
M
Claim
3
Suppose
v
,
r
for all i ∈ I. Then© #C2 = 2. Moreover,
if
g
<
1
2
¡ M ¢
ª
i
i
p1 = g , 0 ,¡then j¢ = P for all i ∈ C2 if and only if # i ∈ I ©
: j = P ≥ 2. ªInstead if p1 = g M , 1 , then j i = A for all i ∈ C2 if and only if # i ∈ I : j i = A ≥
2.
Proof of Claim 3. That #C2 = 2 follows from ego rents decreasing with the
number of parties
in the coalition
and each party having veto power.
©
ª
Let S ≡ i ∈ I : j i = P . If #S = 3 or = 0, it is trivial.
© ª
Suppose #S = 2. Note that g1 = g M implies P (C2 , g1 ) = g M , and thus
g2 = g M for all C2 ∈ WC . First suppose r1 = 0. Then for any C2 ∈ WC with k ∈ C2
and k ∈
/ S, r2 = 0 (since σ k2 (A) = 0). Instead ¡if k ∈
/ C2 , then
ji =
P for all¢ i ∈ C2 ,
¢
¡ M
i
i
M
i
and r2 = 1 (since σ 2 (P ) = 1). Given that
u
,
1,
m
, 0, m2 for all
g
>
u
g
2
P¢
P
¡
i ∈ S, we thus have C2 = S and p2 = g M , 1 . Indeed, if party i ∈ S is the first
to be appointed as the formateur, it proposes party h ∈ S, h 6= i, to join it in a
coalition, and party h accepts. Instead if party k ∈
/ S is the first to be appointed
as the formateur, then the other two parties are better off rejecting its offer since
they anticipate that one of them will then be appointed as the formateur and will
propose the other one to join it in the second-period government.
Suppose instead r1 = 1. Then for any C2 ∈ WC , there exists i ∈ C2 such
¡ that¢
j i = P . Hence that party vetoes the repeal of the reform, and thus p2 = g M , 1
for all C2 ∈ WC .
It remains to consider the case where #S = 1. The argument is similar to the
one where #S = 2, but with C2 = I\S if r1 = 1. ¥ Q.E.D.
22
©
ª
Lemma 2. Suppose v i (g1 , 1) < N2+1 for all i ∈ I and #¡ i ∈ I¢ : j i = P ≥ 2.
Then there exists an equilibrium of the subgame where p2 = g M , 1 .
ª
©
Proof. Let # i ∈ I : j i = P ≥ 2 and v i (g1 , 1) < N2+1 for all i ∈ I. Since at
least two parties are pro-reform, there is a pro-reform party i in any second-period
coalition government C2 , which thus vetoes a repeal of the reform. Hence in any
equilibrium of the subgame, r2 = 1.
It remains to show that there exists an equilibrium of the subgame where g2 =
g M . °Suppose° first
g1° < g L . Define ge > g L the level of public good such
° that
L
L
°
°
°
that g − ge = g − g1 °. There are two cases to consider. Either ge ≥ g M , in
which case g M ∈ P (C2 , g1 ) for all C2 ∈ WC , and γ i2 (C2 , g1 ) = g M for all i ∈ C2 is
an equilibrium strategy in the second-period policy choice game. Or ge < g M . In
R
M
that case g M ∈ P ({M, R} , g1 ), and γ M
are
2 ({M, R} , g1 ) = γ 2 ({M, R} , g1 ) = g
equilibrium strategies in the second-period policy choice game (in fact g£2 = g¤M is
also the Nash Bargaining solution here). In the same time P (C2 , g1 ) = g L , ge for
all C2 ∈ WC with L ∈ C2 . It follows that parties M and R are strictly better off
forming a ¡coalition
¢ government together than with party L. And thus C2 = {M, R}
and p2 = g M , 1 is an£ equilibrium
outcome of the subgame.
¢
Suppose now g1 ∈ g L , g M , then P (C2 , g1 ) = {g1 } for all C2 ∈ WC with L ∈ C2 ,
and the same argument
as
¡
¢ above
© applies.
ª
If g1 = g M , P C2 , g M = g M for all C2 ∈ WC and thus g2 = g M .
Finally, the case g1 > g M is symmetric to the one where g1 < g M . Q.E.D.
We now turn to proving the propositions.
L
M
the mid-point between g L and g M ,
Proof of Proposition 1. Let g LM ≡ g +g
2
¢
¡
and consider the class of distributions of preference-types F where F g LM < N2+1 .
Also define θ as follows
n
o gR − gL
θ ≡ max θM , θR , e
θ +
βP
, where e
θ is the initial belief that at least two parties are pro-reform. Condition (i)
and θi ∈ (0, 1) for each party i imply θ ∈ (0, 1). Suppose θL > θ.
¡ M ¢
I am going
¡ L toL ¢show that there exists a political equilibrium with p1 = g , 0
and p2 = g , r
as the policy outcome, with party L winning outright in the
election and forming a single-party government in the second period of the game.
Since the second-period policy choice is the last stage of the game, no party
i has an incentive
to propose a reform outcome different from the one it prefers.
¡ ¢
Hence σ i2 j i = ri . Also if party i is the only party in office in the second period,
it will implement its preferred level of public spending that is, γ i2 ({i} , g1 ) = g i .
Finally letting γ i2 (C2 , g1 ) be any equilibrium public spending strategy for party i
whenever C2 6= {i}, we have (σ 2 , γ 2 ) is an equilibrium profile of strategies in the
second-period policy choice game.
Let the government formation strategies be as described in the paper.
I am now going to show that there exists a SNE of the voting game, and that in
any SNE the profile of voting strategies α must be such that: (i) v L (g, 1) < N2+1
¢
¡
N+1
R
for all g; (ii) v L g M , 0 ≥ N+1
for all g 6= g M . Let α be
2 ; and (iii) v (g, 0) ≥ 2
23
a profile of voting strategies such that for any pro-reform citizen n,
⎧ n
, for all g
⎨ α (M
¡ ; g, 1) ¢= 1
αn L; g M , 0 = 1
⎩ n
α (R; g, 0) = 1
, for all g 6= g M
, and for any anti-reform citizen n and all g,
½ n
α (R; g, 1) = 1
αn (M ; g, 0) = 1.
Also let the beliefs be as described in the paper.
I now prove the result via a sequence of three claims.
¢
¡
Claim 1 v L g M , 0 ≥ N2+1 .
¡
¢
¢
¡
Proof of Claim 1. Let p1 = g M , 0 . Given α, v L g M , 0 ≥ N2+1 . Hence
C2 = {L}, and citizens anticipate g2 = g L and r2 = 1 (0, resp.) with probability
θL (1 − θL , resp.).
¢
¡
To show that α is an equilibrium profile of voting strategies and v L g M , 0 ≥
N +1
the unique SNE outcome of the voting game, it ³is sufficient
to show that
2
´
neither of the pro-reform citizens prefer to the lottery g L , θL any of the other
³
³
´
´
¢
¡
lotteries: (i) g M , θM , the expected lottery if v M g M , 0 ≥ N2+1 ; (ii) g R , θR ,
³
´
¢
¡
the expected lottery if v R g M , 0 ≥ N2+1 ; or (iii) g M , e
θ , the expected lottery
n
o
¢
¡
if v i g M , 0 < N+1
for all i ∈ I (by lemma 1). Letting b
θ ≡ max θM , θR , e
θ , a
2
sufficient condition is that for all pro-reform citizens,
°
°
°ª
© °
− °g − g L ° + θL β P > max
θ βP
− °g − g ° + b
g∈{g M ,g R }
R
L
, or θL > b
θ + g β−g . Since the RHS of this latter inequality is θ, and that θL > θ,
P
the condition is satisfied. ¥
Claim 2 v L (g, 1) < N2+1 for all g ∈ [0, 1].
Proof of Claim 2. Let p1 = (g, 1). Given α, v M (g, 1) ≥ N2+1 and thus
v L (g, 1) < N2+1 . Hence C2 = {M }, and citizens anticipate g2 = g M and r2 = 1. To
show that α is an equilibrium profile of voting strategies it is sufficient to show that
there is no coalition of voters which is sufficiently large and would prefer any
³ of the
´
¡ L ¢
N+1
L
other lotteries: (i) g , 1 , the expected lottery if v (g, 1) ≥ 2 ; (ii) g R , θR ,
¡
¢
the expected lottery if v R (g, 1) ≥ N2+1 ; or (iii) g M , 1 , the expected lottery if
¡
¢
for all i ∈ I (by lemma 2). This holds given F g LM < N2+1 and
v i (g, 1) < N+1
2
R
M
θR < 1 − g β−g (the latter inequality by assumption 1(ii)). Hence there exists a
P
SNE of the voting game where v L (g, 1) < N2+1 .
It remains to show that v L (g, 1) < N2+1 in any SNE. Suppose on the contrary
that there exists an equilibrium profile of voting strategies α where party L gets a
majority of votes. It follows that C2 = {L}, and citizens anticipate g2 = g L and
r2 = 1. Now construct a profile of voting strategies α
e where¡α
e n (M
¢ ; g, 1) = 1 for all
n
n
n
LM
citizens n with g > g , and α
e = α otherwise. Since F g LM < N2+1 party M
thus gets a majority of votes when p1 = (g, 1). It is easy to see that any citizen n
24
with α
e n (M ; g, 1) = 1 then gets a strictly higher expected second-period utility than
under α, which contradicts α an equilibrium profile of voting strategies. Hence in
any SNE of the voting game v L (g, 1) < N2+1 . ¥
Claim 3 v R (g, 0) ≥
N +1
2
for all g 6= g M .
R
L
Proof of Claim 3. Similar to the proof of Claim 1, with θR > g β−g a
P
sufficient condition for v R (g, 0) ≥ N2+1 , g 6= g M , to be the unique SNE outcome of
the voting game (this condition holds
¡ by ¢assumption 1(ii)). ¥
It remains to show that p1 = g M , 0 is an equilibrium outcome of the firstperiod policy choice game. Let (σ 1 , γ 1 ) be any weakly undominated
¡ L
¢profile of
M
R
strategies in the first-period policy game, with σ L
(J
)
=
σ
,
A,
j
j
= 0 and
1
1
3
L
M
γ 1 (J , 0) = g for all J ∈ {P, A} . The next two claims show that (σ 1 , γ 1 ) is an
equilibrium profile.
3
M
Claim 4 γ L
for all J ∈ {P, A} .
1 (J , 0) = g
M
Proof of Claim 4. Suppose r1 = 0. I have to show that γ L
1 (J , 0) = g
¡ Mis a¢
M
M
best response to γ 1 (J , 0). Suppose party L proposes g1 = g , then p1 = g , 0
¢
¡
, 0 ≥° N+1
L’s intertemporal
utility is thus equal to
and¡v L g M
2 (by°Claim 1). Party
¢
¡
¢
UjL g M , 0 = − °g L − g M ° + m2 + δ β j rL + m1 , where rL is party L’s preferred
reform outcome. Now suppose instead that party L proposes g 6= g M . Either party
M proposes g 6= g, and thus g1 = g M (since g0 = g M ). Or, party M proposes g = g
in which case g1 = g and v R (g, 0) ≥ N+1
intertemporal
2 (by Claim 3). The maximal
°
¡ °
¢
utility party L can then get is equal to max UjL (g, 0) = m2 +δ − °g L − g R ° + β j rL
(which would happen if g1 = g L and rR = rL ). Thus, a sufficient condition for
party L not having an incentive to deviate is
°
°
°
¡
¡ °
¢
¢
− °g L − g M ° + m2 + δ β j rL + m1 ≥ m2 + δ − °g L − g R ° + β j rL
¡
¢
¡
¢
, or δ m1 ≥ g M − g L − δ g R − g L , which is satisfied by condition (ii). ¥
¡ L
¢
3
M
Claim 5 σL
j , A, j R = 0 for all J ∈ {P, A} .
1 (J ) = σ 1
Proof of Claim 5. (1) Consider first a pro-reform party L. If it chooses to
veto the adoption of ¡the reform,
then r1 = 0 and by Claim 4, g1 = g M . By
¢
N +1
L
M
Claim 1, we¡ have ¢v g °, 0 ≥ °2 and party L’s intertemporal utility is thus
equal to UPL g M , 0 = − °g L − g M ° + m2 + δ (β P + m1 ). Rather if it deviates and
implement the reform, then with probability (1 − π), party M vetoes the adoption
of the reform and r1 = 0. But with probability π, r1 = 1 and v M (g, 1) ≥ N+1
2 . The
maximum intertemporal utility party L can get is max UPL (g, 1) = β P + m2 + δβ P
(which would happen if g1 = g L ). A sufficient
¡ condition
¢ for a pro-reform party L
M R
not having an incentive to deviate from σ L
,
j
P,
j
= 0 is
1
¡
¡
¢
¢
UPL g M , 0 ≥ (1 − π) UPL g M , 0 + π max UPL (g, 1)
¡
¢
, or δ m1 ≥ β P + g M − g L . The latter inequality is satisfied by condition (ii).
(2) Consider now an anti-reform
° L. The° logic is the same as for a pro¢ party
¡
reform party L but with UAL g M , 0 = − °g L − g M °+m2 +δ m1 and max UAL (g, 1) =
β A + m2 . Hence a sufficient ¡condition ¢for an anti-reform party
¢having an
¡ ML not
M R
L
incentive to deviate from σL
A,
j
=
0
is
δm
, which is
,
j
≥
β
+
g
−
g
1
A
1
satisfied since β A < 0 < β P .
25
(3) Finally, consider an anti-reform¡ party¢ M.38 If it vetoes the adoption of
N +1
the reform, r1 = 0, g1 = g M and v L g M
,0 ≥
its minimal
2 . As a
°
°
¢
¡ result,
¡
¢
intertemporal utility is equal to min UAM g M , 0 = m2 + δ − °g M − g L ° + β A
(which would happen if j L = P ). Rather, if it deviates and implements the reform, then with probability (1 − π), party L vetoes the adoption of the reform and
r1 = 0. But with probability π,¡ r1 = ¢1 and v M (g, 1) ≥ N+1
2 . Therefore, party
M’s intertemporal utility is UAM g M , 1 = β A + m2 + δ m1 . Hence,
¡ L a sufficient
¢
M
condition for party M not having an incentive to deviate from σ 1 j , A, j R = 0
¡
¢
δ
m1 + g M − g L , which is satisfied by assumption 1(i). ¥ Q.E.D.
is |β A | ≥ 1−δ
Proof of Proposition 2. Consider the class
of ¢distributions of preference types
¡ M ¢F
¡ LM
N+1
<
g
,
;
(b)
N
>
max{F
that satisfy the following
conditions:
(a)
F
g
A
P
³
³
´ 2 ´i
h ¡ ¢
¡ M¢
¡ M¢
h
N +1
θ−θL
M
LM
b
NP −FP g }; (c) FP g
+
|β A | < 2 ; and (d) [FP g +
+ FA g
2
³ R ´
´
³
h
θ
−
θ
N
+1
FbA g MR +
|β A | ] ≥ 2 , where Fbj (g) ≡ # {n : j n = j and g n < g} for
2
j ∈ {P, A} and g MR =
g M +g R
.
2
Also define θ as follows
(
(
¯ ))
¯ k
¯g − g M ¯
e
θ−
θ ≡ max 0, max
.
|β A |
k∈{L,R}
n
o
θ (this holds by condition (i)) and min θL , θR > θ.
Suppose θM < e
show
that there exists a political equilibrium with p1 =
¡ MI am
¢ now going¡ to
¢
M
g
,
0
and
p
=
g
,
1
if
at
least two parties are pro-reform, and p1 = p2 =
2
¡ M ¢
g , 0 otherwise.
Since the second-period policy choice is the last stage of the game neither party
has an incentive
to propose a reform outcome different from the one it prefers.
¡ ¢
Hence σi2 j i = ri for any party
i. ¢Also if g1 = g M proposing its ideal level
¡
i
of public spending that is, γ 2 C2 , g M = g i , is an equilibrium strategy for each
party i. Finally letting γ i2 (C2 , g1 ) be an arbitrary equilibrium strategy for party i
whenever g1 6= g M , we have that (σ 2 , γ 2 ) is an equilibrium profile of strategies in
the second-period policy choice game.
Let the government formation strategies be as described in the paper, and satisfy
lemmas 1 and 2.
I am now going to show that there exists a SNE of the voting game
where
the
¢
¡
electoral outcome is such that: (i) v M (g, 1) ≥ N2+1 for all g; (ii) v i g M , 0 < N2+1
for any party i; and (iii) v R (g, 0) ≥ N+1
for all g 6= g M . Let α be the
2
¡ profile¢ of
voting strategies described in the proof of Proposition 1 except that αn R; g M , 0 =
1 for all pro-reform citizens n with g n > g M . Hence
¡ M the
¢ proof is similar to Claims 2
and 3 in
the
proof
of
Proposition
1
when
p
=
6
g
,
0
. We thus only have to prove
1
¡
¢
that α .; g M , 0 is a SNE profile of voting strategies. This is done in the following
claim.
¡
¢
Claim 1 α .; g M , 0 is an equilibrium
¡ profile
¢ of voting strategies.
Proof of Claim 1. Let p1 = g M , 0 . Given the class of distributions of
¢
¢
¡
¡
for any party i, and v M g M , 0 >
preference types F , 0 < v i g M , 0 < N+1
2
3 8 Note that since σ L (J ) = 0 for all J ∈ {P, A}3 , r = 0 whatever party M’s decision. But
1
1
remember that we have imposed
incumbents’
strategies to be weakly undominated. Hence, we
still have to show that σM
j L , A, j R = 0 is an equilibrium strategy.
1
26
© ¡
¢
¢ª
¡
max v L g M , 0 , v R g M , 0 . Hence #C2 = 2, and citizens anticipate g2 = g M
and r2 = 1 (0, resp.) with probability e
θ (1 − e
θ, resp.).
¡
¢
For α to be an equilibrium profile of voting strategies when p1 = g M , 0 , it
must be that there is no coalition of voters who are pivotal and want to deviate, i.e.
no coalition of voters who prefer
second-period
³ one of´the following lotteries over the
¢
¡
policy outcome is pivotal: (i) g L , θL , the expected lottery if v L g M , 0 ≥ N2+1 ;
³
³
´
´
¢
¡
R R
(ii) g M , θM , the expected lottery if v M g M , 0 ≥ N+1
;
or
(iii)
g
,
θ
, the
2
¡ M ¢ N +1
R
expected lottery if v g , 0 ≥ 2 .
Consider first the coalition of voters who might prefer party L to win outright.
For any such citizen n it must be that
°
°
°
°
− °g n − g L ° + θL β n ≥ − °g n − g M ° + e
θ βn.
If citizen n is pro-reform, this inequality together with condition (i) imply g n <
g . And if citizen n is anti-reform, θL > θ implies that this inequality can hold
´
³
M
L
(hθ−θL ).|β A |
θ ≤ g −g and g n ≤ g LM +
. But given F this coalition
only if θL − e
M
|β A |
2
of citizens is not pivotal for party L getting a majority of votes.
Since θM < e
θ only the anti-reform citizens want party M to win outright, and
they already vote for that party. Hence no coalition of voters is pivotal for party M
getting a majority of votes and is willing to deviate in order to achieve this. Finally
proceeding as we did for party L, it is possible to show that, given condition (d) on
F , the coalition of citizens who might prefer party R to win outright is not pivotal.
Those three cases exhaust all possibilities. Hence there is no coalition of voters
who are pivotal and want
¡ to¢deviate. Therefore α is an equilibrium profile of voting
strategies when p1 = g M , 0 . ¥ ¡
¢
It remains to show that p1 = g M , 0 is an equilibrium outcome of the firstperiod policy choice game. Let
of weakly undominated
¡ L(σ 1 , γR1¢) be any profile
M
M
strategies, with σ L
for all r1 ∈
j , A, j
= 0 and γ M
1 (J ) = σ 1
1 (J , r1 ) = g
3
{0, 1} and J ∈ {P, A} . The next two claims show that those are equilibrium
strategies in the first-period policy choice game.
M
Claim 2 γ M
for all r1 ∈ {0, 1} and J ∈ {P, A}3 is a best response
1 (J , r1 ) = g
to γ L
1 (J , r1 ).
Proof of Claim 2. (1) Suppose that r1 = 1. From the voting stage, we
have v M (g, 1) °≥ N+1
utility is equal to
2 °for all g and party
¡ M’s intertemporal
¢
UjM (g, 1) = − °g M − g ° + β j + m2 + δ β j rM + m1 . But UjM (g, 1) reaches its
M
(unique) maximum at g = g M . Hence, γ M
is a best response to
1 (J , 1) = g
3
L
γ 1 (J , 1) for all J ∈ {P, A} .
M
(2) Suppose that r1 = 0. Consider first¡a pro-reform
party
¢
© L ¡M.MIf it
¢ proposes
¡ M g¢ª,
N −1
M
M
M
R
then g1 = g . It follows that 2 ≥ v
g , 0 > max v g , 0 , v g , 0 ,
which implies #C2 = 2 and M ∈ C2 (if j L = j R , C2 = {L, M } with probability
1/2 and C2 = {M, R} with probability 1/2. Otherwise, C¡2 = {M,
¢ k} with k ∈ I
M
M
and j k = P ). Party M’s¡ intertemporal
g
utility
will
be
U
,
0
= (1 + δ) m2 if
P
¢
j L = j R = A, and UPM g M , 0 = m2 + δ (β P + m2 ) otherwise. Instead, suppose
that party M deviates and proposes g 6= g M . Either party L proposes gb 6= g, and
g1 = g M . Or party L proposes g, and thus g1 = g. From the voting stage we
have v R (g, 0) ≥ N2+1 , and party M’s intertemporal utility is equal to UPM (g, 0) =
°
°
°
¡ °
¢
¡
¢
− °g M − g ° + m2 + δ − °g M − g R ° + β P rR . For all j L , j R ∈ {P, A}2 , we have
27
¢
¡
that UPM g M , 0 > UPM (g, 0) ¡for all g 6= g¢M . Hence, a pro-reform party M has no
incentive to deviate from γ M
j L , P, j R , 0 = g M .
1
Consider now an anti-reform party M. If there exists k ∈ {L, R} such that
j k = A, then the argument is similar to the one for a pro-reform party M. Suppose
instead that j L = j R = P . If party M proposes g M , then ¡g1 = g¢M . From the voting
stage and lemma 1, we have that C2 =¡ {L, R}
and p2 = g M , 1 . Hence, party M’s
¢
intertemporal utility is equal to UAM g M , 0 = m2 + δ β A . Instead, if parties L
¡
¢
p2 =° g R , 1 .
and M agree on g1 6= g M , then v R (g1 , 0) ≥ N2+1 , C2 = {R} and
°
M
Party
intertemporal
− ¢°g M − g ° + m2 +
°
¡ °M’s
¢ utility is then equal to UA (g,M0)¡ =
M
R
M
δ − °g − g ° + β A , which is strictly lower than ¡UA g , 0 ¢. Hence, an antireform party M has no incentive to deviate from γ M
j L , A, j R , 0 = g M . ¥
1
¡ L
¢
M
Claim 3 σL
j , A, j R = 0 for all J ∈ {P, A}3 .
1 (J ) = σ 1
Proof of Claim 3. (1) Consider first a pro-reform party L. If it vetoes the
adoption
reform in period 1, then r1 = 0, g1 = g M (by Claim 2) and
¡ M ¢ of the
N+1
i
v g , 0 < ¡2 for¢ all i ∈
utility is¢ at
°
° I. As a° result, party
¡ °L’s intertemporal
least min EUPL g M , 0 = − °g L − g M ° + m2 + δ − °g L − g M ° + β P rM + m22 .39
Now if party L implements the reform, then with probability (1 − π), party M
vetoes the adoption of the reform and r1 = 0. But
¡ with
¢ probability
¡ π,¢party M
proposes to adopt the reform. In that case, p1 = ¡g M , 1 ¢ and v°M g M , 1 ° ≥ N2+1 .
L
M
M°
° L
Party L’s¡ intertemporal
+ βP +
° utilityMis¢thus equal to UP g , 1 = − g − g
° L
M
m2 + δ − °g − g ° + β P r . Hence, a sufficient
condition
for
a
pro-reform
¡
¢
M R
party L not having an incentive to deviate from σ L
= 0 is δ m22 ≥ β P ,
1 P, j , j
which holds by condition (ii).
(2) Consider an anti-reform party L. There are three cases to consider. First,
let j M = j R =¡ P . If
then
C2 =
°
¢ party° L vetoes° the adoption
¡ °of the reform,
¢
{M, R} and UAL g M , 0 = − °g L − g M ° + m2 + δ − °g L − g M ° + β A . Instead
if both party ¡L and¢party °M decide°to implement the¡ reform,
then° r1 = ¢1, C2 =
°
{M ¡} and ¢UAL g M , 1¡ = −¢°g L − g M ° + β A + m2 + δ − °g L − g M ° + β A . Since
UAL g M , 0 > UAL g M , 1 , an anti-reform party L has no incentive to deviate.
Second, let j M = P and j R = A. Then, we have C2 = {L, M } with probability 1/2 and {M,¡R} with
1/2.
Party L’s
utility
is
°
°
° L
°
¢ probability
¡ intertemporal
¢
L
M
°g − g M ° + m2 + δ − °g L − g M ° + m2 , and
thus equal
to
EU
,
0
=
−
g
A
2
¢
¢
¢
¡
¡
¡
EUAL g M , 0 > UAL¡ g M , 1¢ . Third,
let j M° = A. Then EUAL¡ g°M , 0 is the
°¢ same as
°
L
M
°g L − g M ° + β A + m2 + δ − °g L − g M ° . Again,
above¡but now
U
,
1
=
−
g
A ¡
¢
¢
EUAL g M , 0 > ¡UAL g M , 1 ¢. Hence, an anti-reform party L has no incentive to
M R
deviate from σ L
= 0.
1 A, j , j
(3) It remains to consider an anti-reform party M. There are two cases to
consider: (i) j L = j R = P ; and (ii) j k = A for some k ∈ {L, R}. In the
first ¡case, ¢if party M vetoes the adoption of the reform, then C2 = {L, R} and
UAM g M , 0 = m2 + δ β A . Instead, if the reform is implemented in the first
¡
¢
and party M’s intertemporal utility is equal to
period,
then
v M g M , 1 ≥ N+1
2
¢
¡
UAM g M , 1 = β A + m2 + δ m1 . Hence, party M has no incentive to deviate
¡ L
¢
δ
m1 , which holds by assumption 1(i). In
j , A, j R = 0 if |β A | ≥ 1−δ
from σ M
1
the second
case,
if
party
M
vetoes
the
adoption
of the reform, then M ∈ C2 and
¢
¡
UAM g M , 0 = m2 + δ m2 . As a result, party M has no incentive to deviate if
3 9 If
J = (P, P, P ) or J = (P, A, A), then prob (L ∈ C2 ) =
then prob (L ∈ C2 ) = 1.
28
1
.
2
If J = (P, A, P ) or J = (P, P, A),
|β A | ≥ δ (m1 − m2 ) which is satisfied by assumption 1(i). ¥ Q.E.D.
Proof of Proposition 3. Consider a class
of distributions
of preference types F
¢ N +1
¡ LM
;
and
(b) [FP (x) + FA (y)] ≥
<
that satisfy the following conditions:
(a)
F
g
2
³ L k´ o
n
N +1
θ −θ
Lk
LC
min
θ, and
g +
β P with g = g LM and θC = e
2 , where x = k∈{M,R,C}
2
³ L k´
© kª
k
L
y =
min
|β A | if θL ≥ θk − g |β−g| (with
y , where y k = g Lk − θ −θ
2
A
k∈{M,R,C}
g C = g M ) and y k = 1 otherwise. Also define θ and θ as follows
⎧
½
¾¾
½
|gk −gL |
⎪
⎪
, and
⎨ θ ≡ max 0, maxk∈{M,R,C} θk − β P
½
¾
¾
½
|gk −gL |
⎪
⎪
,1 .
⎩ θ ≡ min mink∈{M,R,C} θk + |β |
A
β P < |β A | (by assumption 1(i) and condition (ii)) and condition (i) imply 0 ≤ θ <
θ ≤ 1.
¡ ¢
Let θL ¡∈ θ, θ¢ . I am going
¡ L toL ¢show that there exists a political equilibrium
M
with p1 = g , 0 and p2 = g , r as the policy outcome, with party L winning
outright in the election and forming a single-party government in the second period.
1, except for Claim 1. Replace
¡ The proof
¢ is similar to the proof
¢
¡ ofMProposition
n
α .; g M , 0 by the following:
α
,
0
=
1
for
all pro-reform citizens n such
L;
g
³ L k´ o
n
¢
¡
that g n ≤
min
g Lk + θ −θ
β P , and αn L; g M , 0 = 1 for all anti-reform
2
k∈{M,R,C}
³ L k´
© kª
min
|β A | if θL ≥
y , where y k = g Lk − θ −θ
citizens n such that g n ≤
2
k∈{M,R,C}
³ L k´ o
n
k
L
g Lk + θ −θ
βP
θk − g |β−g| and y k = 1 otherwise. It can be shown that min
2
A
k∈{M,R,C}
is strictly greater than g L given that θL >©θ, and
strictly lower than g M since θL < θ
ª
and |β A | > β P . Also, we have
min
y k > g L since θL < θ.
k∈{M,R,C}
¢
¡
Given the class of distributions F defined above, v L g M , 0 ≥ N2+1 . Now it is
sufficient to³show that
´ none of the citizens who vote for party L strictly prefers to
L L
the lottery g , θ
they expect when party L gets the absolute majority of votes,
³
´
¢
¡
any of the other feasible lotteries, i.e. (i) g M , θM if v M g M , 0 ≥ N2+1 ; (ii)
³
´
³
´
¡
¡
¢
¢
g R , θR if v R g M , 0 ≥ N2+1 ; or (iii) g M , e
θ if v i g M , 0 < N2+1 for all i ∈ I.
Consider first those
citizens
³
´ who
³ are ´of the pro-reform type. For them to strictly
M
M
prefer the lottery g , θ
to g L , θL , it must be that
°
°
°
°
− °g n − g M ° + θM β P > − °g n − g L ° + θL β P .
M
L
Now for those citizens n with g n ≤ g L , it must be that θL < θM − g β−g , which
P
¢
¡
contradicts θL³ > θ. ´For those citizens n with g n ∈ g L , g M , it must be that
L
M
g n > g LM + θ −θ
β P , again a contradiction since we consider citizens with
n2
³ L k´ o
gn ≤
g Lk + θ −θ
β P . In a similar way, we can show that neither
min
2
k∈{M,R,C}
´
³
³
´
³
´
θ to g L , θL .
of those citizens prefer g R , θR or g M , e
29
Consider
now
³
´ those
³ citizens
´ who are of the anti-reform type. For them to strictly
M
M
L L
prefer g , θ
to g , θ , it must be that
°
°
°
°
− °g n − g M ° + θM β A > − °g n − g L ° + θL β A .
M
L
For those citizens with g n < g L , it must be that θL > θM + g |β−g| , which conA
£ L M¤
n
tradicts θL < θ. ³For those
with
g
∈
g
,
g
,
the
above
condition
implies
´
L
M
g M −g L
θL −θM
n
LM
that g > g
|β A |. Either θ ≥ θ − |β | in which case this
−
2
A
³ L M´
L
M
g M −g L
contradicts g n ≤ g LM − θ −θ
|.
Or,
θ
<
θ
−
in which case
|β
A
2
|β A |
h
³ L M´
i
g LM − θ −θ
|β A | > g M and the condition requires g n > g M , which contra2
£
¤
n
M
dicts g n ∈ g L , g M . Finally, for those
³ L with
´ g > g , the above condition implies
M
L
M
θL > θM − g |β−g| . But then g LM − θ −θ
|β A | < g M which contradicts g n > g M
2
A
³ L M´
and g n ≤ g LM − θ −θ
|β A |. In a similar way, we can show that neither of those
2
³
´
³
´
³
´
R R
citizens prefer g , θ
θ to g L , θL . Q.E.D.
or g M , e
Proof of Proposition 4. Consider the same class of distributions of
¡ preference
¢
types than in Proposition 2, replacing condition (b) by NA > max{FP g M , NP −
¡ LM ¢
FP g
}. Also, define θ as follows
(
(
¯ ))
¯ k
¯g − g M ¯
e
θ ≡ max 0, max
θ−
.
|β A |
k∈{L,R}
n
o
θ (which holds by condition (i)) and min θL , θR > θ.
Suppose θM < e
¡
¢
¡
¢
There exists a political equilibrium where p1 = ¡g M , 0 ¢, and p2 = g M , 1 if
at least two parties are pro-reform, and p1 = p2 = g M , 0 otherwise. Moreover
neither party gets a majority of votes in the election, and a coalition government
is in office in the second period.
Define the following strategies and beliefs:
(i) Let (σ 2 , γ 2 ) be an¡ equilibrium
profile
in the second-period policy
¢
¡ of strategies
¢
choice game, with σ i2 j i = ri and γ i2 C2 , g M = g i for any party i and government
C2 .
(ii) Let the government formation be as described in the paper.
(iii) Let α be the profile of voting strategies described in the proof of Proposition
1, except that for any pro-reform citizen n,
¢
½ n¡
α ¡L; g M , 1 ¢= 1 if g n ≤ g LM
αn M ; g M , 1 = 1 if g n > g LM
¢
½ n¡
α ¡L; g M , 0 ¢ = 1 if g n ≤ g M
αn R; g M , 0 = 1 if g n > g M .
(iv) Let (σ 1 , γ 1 ) be an equilibrium¡ profile of¢ strategies in the first-period policy
L
M R
M
choice game, with σ M
for all
= 0 and γ M
1 (J ) = σ 1 A, j , j
1 (J , 0) = g
3
J ∈ {P, A} .
(v) Finally, let the beliefs be as described in the paper.
30
The key elements of the proof that those strategies and beliefs constitute a
political equilibrium closely paralell those used in the previous proofs, and are not
repeated. Q.E.D.
31